• ETRI Journal
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• v.20 no.4
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• pp.327-345
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• 1998

This paper deals with the problem of one-to-one mapping of 2$^n$ task modules of a parallel program to an n-dimensional hypercube multicomputer so as to minimize the total communication cost during the execution of the task. The problem of finding an optimal mapping has been proven to be NP-complete. First we show that the mapping problem in a hypercube multicomputer can be transformed into the problem of finding a set of maximum cutsets on a given task graph using a graph modification technique. Then we propose a repeated mapping scheme, using an existing graph bipartitioning algorithm, for the effective mapping of task modules onto the processors of a hypercube multicomputer. The repeated mapping scheme is shown to be highly effective on a number of test task graphs; it increasingly outperforms the greedy and recursive mapping algorithms as the number of processors increases. Our repeated mapping scheme is shown to be very effective for regular graphs, such as hypercube-isomorphic or 'almost' isomorphic graphs and meshes; it finds optimal mappings on almost all the regular task graphs considered.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.5
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• pp.1110-1115
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• 2014

The matrix-star and the transposition graphs are considered as star graph variants that have various merits in graph theory such as node symmetry, fault tolerance, recursive scalability, etc. This paper describes an one-to-one mapping algorithm from a matrix-star graph to a transposition graph using adjacent properties in graph theory. The result show that a matrix-star graph $MS_{2,n}$ can be embedded in a transposition graph $T_{2n}$ with dilation n or less and average dilation 2 or less.

• The Transactions of the Korea Information Processing Society
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• v.3 no.4
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• pp.766-780
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• 1996

This paper presents a mapping scheme for parallel processing using an accurate characterization of the communication overhead. A set of objective functions is formulated to evaluate the optimality of mapping a problem graph into a system graph. One of them is especially suitable for real-time applications of parallel processing. These objective functions are different from the conventional objective functions in that the edges in the problem graph are weighted and the actual distance rather than the nominal distance for the edges in the system graph is employed. This facilitates a more accurate qualification of the communication overhead. An efficient mapping scheme has been developed for the objective functions, where two levels of assignment optimization procedures are employed: initial assignment and pairwise exchange. The mapping scheme has been tested using the hypercube as a system graph.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1105-1114
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• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.

• The Transactions of the Korea Information Processing Society
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• v.5 no.11
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• pp.2823-2834
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• 1998

This paper deals with the problem of one-to-one mapping of $2^n$ task modules of a parallel program to an n-dimensional hypercube multicomputer so as to minimize to total communication cost during the execution of the task. The problem of finding an optimal mapping has been proven to be NP-complete. We first propose a graph modification technique which transfers the mapping problem in a hypercube multicomputer into the problem of finding a set of maximum cutsets on a given task graph. Using the graph modification technique, we then propose a repeated mapping scheme which efficiently finds a one-to-one mapping of task modules to a hypercube multicomputer by repeatedly applying an existing bipartitioning algorithm on the modified graph. The repeated mapping scheme is shown to be highly effective on a number of test task graphs, it increasingly outperforms the greedy and recursive mapping algorithms as the number of processors increase. The proposed algorithm is shown to be very effective for regular graph, such as hypercube-isomorphic or 'almost' isomorphic graphs and meshes; it finds optimal mapping on almost all the regular task graphs considered.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.441-453
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• 2021

In this work, we define the concept of a mixed G-monotone mapping on a modular metric space endowed with a graph, and prove some fixed point theorems for this new class of mappings. Results of this paper extend coupled fixed point theorems from partially ordered metric spaces into the modular metric spaces endowed with a graph. An example is presented to illustrate the new result.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.497-504
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• 2009

We introduce the concepts of M-preclosed graph and M$^*$-preopen mapping on spaces with minimal structures and investigate some properties of M$^*$-preopen mapping. We also investigate the relationships between M-precontinuous mappings and several types of m-compactness.

• Journal of the Korea Society of Computer and Information
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• v.3 no.4
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• pp.44-48
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• 1998

In this paper proposed Component Synthesis Algorithm(CSA) for mapping described HDL to RT component of given library. CSA transform I/O variables of HDL and relation of operators to control/data flow graph(CDFG) that consists of graph, reduce the size of graph, compute the cost, the bound, and the method that use compatibility graph(CG), and then mapping to component. Component synthesis used branch-and-bound algorithm. The result that synthesis using CSA algorithm was proved that this result and the cost of the manual were indentified.

• Korean Journal of Construction Engineering and Management
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• v.17 no.3
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• pp.32-42
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• 2016

In Korea, the absence of BIM use in existing civil structures and buildings is driving a demand for as-built BIM. As-built BIMs are often created using laser scanners that provide dense 3D point cloud data. Conventional static laser scanning approaches often suffer from limitations in their operability due to the difficulties in moving the equipment, the selection of scanning location, and the requirement of placing targets or extracting tie points for registration of each scanned point cloud. This paper aims at reducing the manual effort using a kinematic 3D laser scanning system based on graph-based simultaneous localization and mapping (SLAM) for continuous indoor mapping. The robotic platform carries three 2D laser scanners: the front scanner is mounted horizontally to compute the robot's trajectory and to build the SLAM graph; the other two scanners are mounted vertically to scan the profiles of surrounding environments. To reduce the accumulated error in the trajectory of the platform through loop closures, the graph-based SLAM system incorporates AdaBoost loop closure approach, which is particularly suitable for the developed multi-scanner system providing more features than the single-scanner system for training. We implemented the proposed method and evaluated it in two indoor test sites. Our experimental results show that the false positive rate was reduced by 13.6% and 7.9% for the two dataset. Finally, the 2D and 3D mapping results of the two test sites confirmed the effectiveness of the proposed graph-based SLAM.

• IEMEK Journal of Embedded Systems and Applications
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• v.11 no.4
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• pp.209-218
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• 2016

This paper proposes a new lifetime aware buffer mapping method of a synchronous dataflow (SDF) graph on a hybrid memory system with DRAM and PRAM. Since the number of write operations on PRAM is limited, the number of written samples on PRAM is minimized to maximize the lifetime of PRAM. We improve the utilization of DRAM by mapping more buffers on DRAM through buffer sharing. The problem is formulated formally and solved by an optimal approach of an answer set programming. In experiment, the buffer mapping method with buffer sharing improves the PRAM lifetime by 63%.